Using EPECs to model bilevel games in restructured electricity markets with locational prices

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context

Equilibrium analysis in imperfect Traders' and GenCos' market

The paper models the strategic behavior of traders, GenCos and ISO using the multi-leader-follower framework. The outcomes of the strategic behavior of the players have been modeled using an equilibrium problem with equilibrium constraints. From a policy perspective it is seen that allowing the GenCos to hold FTRs may be welfare enhancing under certain demand conditions and ownership patterns of transmission rights and generation assets. The proposed model has been simulated on a 3 bus system. © 2010 IEEE.published_or_final_versionThe IEEE/PES Transmission and Distribution Conference and Exposition, New Orleans, LA., 19-22 April 2010. In Conference Proceedings, 2010, p. 1-

Complementarity, not optimization, is the language of markets

Each market agent (producer or consumer) in a power market pursues its own objective, typically to maximize its own profit. As such, the specific behavior of each agent in the market is conveniently formulated as a bi-level optimization problem whose upper-level problem represents the profit seeking behavior of the agent and whose lower-level problem represents the clearing of the market. The objective function and the constraints of this bi-level problem depend on the agent's own decision variables and on those of other agents as well. Understanding the outcomes of the market requires considering and solving jointly the interrelated bi-level problems of all market agents, which is beyond the purview of optimization. Solving jointly a set of bi-level (or single-level) optimization problems that are interrelated is the purview of complementarity. In this paper and in the context of power markets, we review complementarity using a tutorial approach

On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling

Modeling several competitive leaders and followers acting in an electricity marketleads to coupled systems of mathematical programs with equilibrium constraints,called equilibrium problems with equilibrium constraints (EPECs). We consider asimplified model for competition in electricity markets under uncertainty of demandin an electricity network as a (stochastic) multi-leader-follower game. First ordernecessary conditions are developed for the corresponding stochastic EPEC based ona result of Outrata [17]. For applying the general result an explicit representation ofthe co-derivative of the normal cone mapping to a polyhedron is derived (Proposition3.2). Later the co-derivative formula is used for verifying constraint qualificationsand for identifying M-stationary solutions of the stochastic EPEC if the demand isrepresented by a finite number of scenarios